Gabor frames and weak duality for Banach spaces of Feichtinger distributions on locally compact abelian groups (Q2754356)

Standard Gabor theory deals with representations of functions in \(L^2(\mathbb{R}^d)\) (or in a class of Banach spaces, called modulation spaces) in terms of time-frequency shifts \(\{e^{2\pi i mbx}g(x-na)\}_{m,n\in\mathbb{Z}}\) of a single function \(g\). A popular choice is to let \(g\) belong to the Feichtinger algebra. Some of the most important results concerning frames of this type are the Janssen representation of the frame operator and the Wexler-Raz relations, which characterize the functionals leading to series expansions of functions in \(L^2(\mathbb{R}^d)\) via the frame. Parts of the theory have already been extended to the case where \(\mathbb{R}^d\) is replaced by a locally compact abelian group; here, further steps in this direction are taken, and (among others) the above results are generalized.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00008].